Naomi B. Robbins on perceptualedge.com states:
A cycle plot (Cleveland, Dunn, and Terpenning, 1978) shows both the cycle or trend and the day-of-the-week or the month-of-the-year effect. Thus the cycle plot retains the strengths more common plots without either of their weaknesses.
Andy Cotgreave provided this example on Tableau.com:
Andy’s blog post to accompany the above video is here:
Jock MacKinlay‘s post from way back in 2008 includes links to a sample workbook:
Bill Saltmarsh includes a video in his post:
Whilst Robert Rouse refers to Cycle plots in this article:
2016 IronViz champion Curtis Harris made use of a Cycle plot, so if that’s not a good enough reason to use one, I don’t know what is! Here’s the winning submission: